Decision Methods in the Theory of Ordinals

Abstract

For an ordinal α, let RS(α), the restricted second order theory of [α, <], be the interpreted formalism containing the first order theory of [α, <] and quantification on monadic predicate variables, ranging over all subsets of α. For a cardinal γ, RS(α, γ) is like RS(α), except that the predicate variables are now restricted to range over subsets of α of cardinality less than γ. ω = ω0 and ω1 denote the first two infinite cardinals. In this note I will outline results concerning RS(α, ω0), which were obtained in the Spring of 1964 (detailed proofs will appear in [8]), and the corresponding stronger results about RS(α, ω1), which were obtained in the Fall of 1964.

Keywords

Congo

Communicated by D. Scott, May 21, 1965

This work was supported in part by grant GP-2754 from the National Science Foundation.

R. McNaughton, Reviews of Weak second order arithmetic and finite automata and On a decision method in restricted second order arithmetic by J. R. Büchi, J. Symb. Logic 28 (1963), 100–102.CrossRefGoogle Scholar